It's a little low. I agree with your calculation. What protocol did you use? You should be able to hit 1e8 to 4e8 or so with a good protocol and care. You may want to electroporate for a library, where it is hard to do worse than 1e9.

The heat shock step is not critical. I've (inadvertently) skipped it many times -- you should still get transformants, though I don't know whether skipping it might have an impact on your efficiency (I don't worry about that because for most of my transformations, a single correct colony is all I need, and homemade competent cells have worked just fine for me in this regard).

I doubt that 50 secs at 44.5 C would have any measurable effect on the viability of your recipients.